\newproblem{lay:4_6_20}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 4.6.20}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Jan. 20th, 2014} \\}{}

  % Problem statement
	Suppose a nonhomogeneous system of six linear equations in eight unknowns has a solution, with two free variables. Is it possible to change some constants on the equations' right
	sides to make the new system inconsistent? Explain.
}{
  % Solution
	If the equation system has a solution with two free variables, it means that the system matrix has rank 6. By changing the right side we cannot make the system inconsistent since for this we would need at least one of the equations to have only 0 coefficients in the left side (which is not possible because the rank of the matrix is 6).
}
\useproblem{lay:4_6_20}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
